Details

sample254.0ms

Algorithm

intervals

Results

175.0ms	139×	body	1280	valid
52.0ms	75×	body	640	valid
7.0ms	17×	body	320	valid
2.0ms	8×	body	160	valid
2.0ms	17×	body	80	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.9b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(sin (- lambda1 lambda2))
4.0b	(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune357.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 7.7b

Counts

73 → 12

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.1b	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff`
2×	`cos-sum` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `sin-cos-mult`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `unsub-neg` `associate-*l/` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
7.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series248.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (cos lambda2))
93.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	348	545
1	1432	476
2	5001	475

prune445.0ms

Filtered

75 candidates to 53 candidates (70.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 0.1b

Counts

87 → 9

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.1b	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity` `sin-mult`
6×	`associate-r` `cos-mult`
5×	`sin-cos-mult`
4×	`frac-times` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `sin-neg` `distribute-rgt-neg-out` `frac-sub` `flip--` `sub-div`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`+-commutative` `flip3-+` `diff-log` `unsub-neg` `associate-*l/` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

6.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
6.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
87.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
184.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	466	1102
1	2150	963
2	5001	960

prune590.0ms

Filtered

90 candidates to 70 candidates (77.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 0.0b

Counts

99 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin (- lambda2))) (cbrt (sin (- lambda2))))
0.6b	(cbrt (sin (- lambda2)))
0.6b	(cbrt (sin (- lambda2)))
0.6b	(cbrt (sin (- lambda2)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (cbrt (sin (- lambda2))) (cbrt (sin (- lambda2))))
2.0ms	(cbrt (sin (- lambda2)))
2.0ms	(cbrt (sin (- lambda2)))
2.0ms	(cbrt (sin (- lambda2)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (sin (- lambda2))) (cbrt (sin (- lambda2))))
110.0ms	(cbrt (sin (- lambda2)))
105.0ms	(cbrt (sin (- lambda2)))
108.0ms	(cbrt (sin (- lambda2)))

simplify115.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	183	633
1	662	562
2	3723	512
3	5002	505

prune516.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

regimes434.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	36
1	38	36

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.9s	4529×	body	1280	valid
1.6s	1989×	body	640	valid
255.0ms	578×	body	320	valid
94.0ms	705×	body	80	valid
64.0ms	199×	body	160	valid